Comparison of Design Properties in Pension Savings

Specialeforsvar ved Alexandra Debel Andreasen

Titel:  Comparison of Design Properties in Pension Savings

Abstract: The properties in savings products have changed in approximately the last 25 years with the main change being from average interest rate savings, often with a guarantee, to market rate savings. The main focus of this thesis is on the effect of different properties of savings products. The three properties studied are guaranteed interest rate, smoothing of the rate of return, and investment strategy. These are analyzed through five different savings types. The properties, smoothing and guarantee, are either applied to a product type or not, whereas the investment strategy is either constant or the life-cycle strategy, Profile C, of the Danish pension company PFA. Some of these product types bare resem-blance to unit link, market rate, or average interest rate savings. A fictitious insured, with 45 years of contributions ending with a 20-year annuity due, is used for the calculations on all five product types. The setup does not include mortality. Simulations are based on a classical Black-Scholes market without time dependent parameters nor multiple risky assets. Numerous simulations are made, where mean, standard deviation, and quantiles are used to compare the reserves and benefits for the product types. Among the findings is the expensiveness of a guarantee as the insured gains very little. Additionally, a smoot-hing of the rate of return has the intended impact, but the smoothing effect used might be too simple with only one insured. It should therefore be used on a larger portfolio. Finally, it is noted that the rate of return in the benefit phase of the lifecycle strategy results in low standard deviation and rarely the highest benefits.

 

 

Vejledere: Mogens Steffensen
                   Nicolai Jonas Maltesen
Censor:     Jesper Olesen, Danica